A path is a small road that connects two places. Paths are usually for people or animals, not large vehicles.
In math, a path is simply a way to connect two points, not necessarily in a straight line.
A railroad is made from two rails laid parallel to each other. The rails are usually fixed to wooden or concretesleepers. Railroads are especially made for trains to travel along.
A road is a long, flat, hard place that vehicles like cars and trucks drive on. Roads connect towns and cities to one another. Roads can be thousands of kilometers long, and be made of hard asphalt, concrete, or just dirt.
A sidewalk, also called a footpath or sometimes a pavement, is a place for people to walk. Sidewalks are usually a thin strip of concrete between people's houses or shops and the road. Cars are not allowed to drive on the sidewalk.
A street, or road in a city or town is a place that people live on, or that has shops on. There are buildings on either side of the street and people walk or drive on the street.
A very narrow street like the one in the picture is sometimes called a lane.